Matrix
Eigenvectors: find eigenvalues, then solve
A−λI=0
Lagrange
dtd​(∂x˙∂L​)−∂x∂L​=0
Structures
Euler Bernoulli
Euler-Bernoulli EquationEuler-Bernoulli Equation · ^Euler-Bernoulli-equation · Embedded block
EIdx2d2y​=F(x)
FEM
Bending Matrix
K=L3EI​​126L−126L​6L4L2−6L2L2​−12−6L12−6L​6L2L−6L4L2​​
K=[1−1​−11​]
K=L3EI​​126L−126L​6L4L2−6L2L2​−12−6L12−6L​6L2L−6L4L2​​
Axial Stress Matrix
K=[1−1​−11​]